-Corresponding parts of congruent triangles are congruent (CPCTC)
Continue to practice 4.4-
4.6 over next several days
4.8
1
-Define: median and discuss altitude, perpendicular bisector, and
angle bisector in a triangle
-Vertex angle bisector conjecture (also altitude, median, and
perpendicular bisector)
3.7
3
-Points of Concurrency: orthocenter, circumcenter, incenter
-Orthocenter: location
-Circumcenter: location, center of circumscribed circle
-Incenter: location, center of inscribed circle
GSP
-Do with 3.8
-Spend 2 days on GSP,
then Euler line GSP,
then a day to review all
conjectures
3.8
3
-Points of Concurrency: centroid
-Centroid: location, distance from vertex and midpoint along median
GSP
-Do with 3.7
-Spend 2 days on GSP,
then Euler line GSP,
then a day to review all
conjectures
Supplement
2
-Euler line: which points are located on it, and how they are
arranged
GSP
GSP pg 191
-Spend 2 days on GSP,
then Euler line GSP,
then a day to review all
conjectures
Supplement
3
-Writing equations of special segments in triangles
-Calculating the coordinate of a POC using system of equations
-Properties of parallelograms
-Opposite angles are congruent
-Consecutive angles are supplementary
-Opposite sides are congruent
-Diagonals bisect each other
Do with 5.6
5.6
1
-Properties of special parallelograms: rectangle, rhombus, and square
-Diagonals of a rhombus are perpendicular and bisect each other
-Diagonals of a rhombus bisect the angles of the rhombus
-Diagonals of a rectangle are congruent and bisect each other
-Any properties true of a rhombus or a rectangle is true of a square
-Properties of kites, trapezoids, and isosceles trapezoids
-Nonvertex angles of a kite are congruent
-Diagonals of a kite are perpendicular
-Diagonal between the vertex angles of a kite is the perpendicular
bisector of the other diagonal
-Vertex angles of a kite are bisected by the diagonal between them
-Consecutive angles between the bases of a trapezoid are
supplementary
-Base angles of an isosceles trapezoid are congruent
-Diagonals of an isosceles trapezoid are congruent
-Midsegments of triangles and trapezoids
-Midsegment of a triangle is parallel to and half the length of the third
side
-The three midsegments of a triangle divide it into four congruent
triangles
-Corresponding parts of similar triangles
-If two triangles are similar then the lengths of the corresponding
special segments are proportional to the lengths of the
corresponding sides
-Angle bisector divides the opposite side into two segments
whose lengths are in the same ratio as the sides of the angle
11.7
1
-Proportional segments between parallel lines
-A line parallel to a side of a triangle divides the other two sides
proportionally
-same with multiple lines
11.3
1
-Indirect measure using similar triangles
Measure statues
or flagpole using
mirrors and
shadows
This section can be done
any day after section 11.2,
depending on the weather
Supplement
2
-Geometric mean
-In a right triangle, the altitude drawn from the right angle is the
geometric mean between the pieces of the hypotenuse
-In a right triangle with an altitude drawn from the right angle, a
leg is the geometric mean between the hypotenuse and the
portion of the hypotenuse adjacent to the let
-Define: image, pre-image, transformation, rigid, isometry,
translation, rotation, reflection, reflectional symmetry, rotational
symmetry, point symmetry
-The line of reflection is the perpendicular bisector of the
segment connecting the pre-image and image
-Properties of transformations
-Reflections: orientation reversed, all measures preserved
-Translations: is the result of double reflection over parallel lines and
the magnitude is twice the distance between those lines; all
measures and orientation preserved
-Rotations: is the result of a double reflection over intersecting lines
and the magnitude is twice the angle formed by the lines; all
measures and orientation preserved
Students struggle with the
idea of equality - "point"
rule vs "equation" rule
Supplement
1
-Translations
Supplement
2
-Rotations
-Define positive and negative degrees of rotation
-Rules for rotating 90, 180, and 270 degrees
Supplement
2
-Compositions
-Composite of two rotations and magnitude, composite of two
translations and magnitude, composite of two reflections and
magnitue
-Using compositions to reflect over lines parallel to the x-axis, the
y-axis, y=x or y=-x
Right Triangles: 14 days
Section
Days
Key Concepts
In Class Activities
Resources
Notes
9.1
1
-Define: hypotenuse, leg
-Pythagorean Theorem
Derive using
geometric mean
Do with 9.2
9.2
1
-Converse of the Pythagorean Theorem
Do with 9.1
Supplement
1
-Pythagorean inequalities: classify a triangle as acute, obtuse, or
right using the Pythagorean Theorem
9.3
2
-Special Right Triangles: 30-60-90, 45-45-90 (isosceles right)
12.1, 12.2 and 9.4 need a
total of 3 days split any
way
12.2, 9.4
2
-Right triangle problem solving
-Define: angle of elevation, angle of depression
Circles:13 days
Section
Days
Key Concepts
In Class Activities
Resources
Notes
1.7
1
-Define: circle, center, radius, chord, diameter, tangent, point of
tangency, concentric circles, arc, major and minor arcs, semicircle,
arc measure, central angle
-Measure of an arc is equal to the measure of its central angle
6.1
1
-A tangent is perpendicular to the radius to the point of tangency
-Tangents from a common point are congruent
6.2
1
-Define (only) inscribed angle
-Congruent chords form congruent central angles and intercepted
arcs
-The perpendicular from the center of a circle to a chord is the
bisector of the cord
-Congruent chords are equidistant from the center
-Perpendicular bisector of a chord passes through the center
6.3
1
-Measure of inscribed angle is half the measure of intercepted arc
-Inscribed angles that intercept the same or congruent arcs are
congruent
-Angles inscribed in a semicircle are right angles
-Opposite angles of a cyclic quadrilateral are supplementary
-Parallel lines intercept congruent arcs
6.4
1
-Proving circle conjectures
Do paragraph proofs
Supplement
1
-Measure of angle formed by two intersecting chords is half the sum
of the measures of the intercepted arcs
-Measure of angle formed by two tangents, two secants, or a
secant and a tangent is half the difference of the measures of the
intercepted arcs
The problems listed under
resources are investigations.
Any application of the
conjectures must be
supplemented
Supplement
1
-When two chords intersect, the product of the segments of one
equals the product of the segments of the other
-When two secants intersect, the product of the outer secant
segment and the whole secant of one, is equal to the product of
the outer secant segment and the whole secant of the other
-When a secant and a tangent intersect, the product of the outer
secant segment and the whole secant is equal to the square of the
tangent
Geometry Honors Using Discovering Geometry
Basics of Geometry: 18 days
-Define: collinear, coplanar, segment, ray, midpoint, bisect
-What is needed to determine unique lines or planes
adjacent
acute, complementary, supplementary, vertical angles, linear pair
endpoints
-GSP 1 Day
-GSP 1 Day
-GSP 1 Day
Triangles: 23 days
-Define: vertex, base, and base angles of isosceles triangles
remote interior angles
-Notes take entire 50 min
-Notes take entire 50 min
4.6 over next several days
angle bisector in a triangle
-Vertex angle bisector conjecture (also altitude, median, and
perpendicular bisector)
-Orthocenter: location
-Circumcenter: location, center of circumscribed circle
-Incenter: location, center of inscribed circle
-Spend 2 days on GSP,
then Euler line GSP,
then a day to review all
conjectures
-Centroid: location, distance from vertex and midpoint along median
-Spend 2 days on GSP,
then Euler line GSP,
then a day to review all
conjectures
arranged
then Euler line GSP,
then a day to review all
conjectures
-Calculating the coordinate of a POC using system of equations
of the days writing equ
of lines
Quadrilaterals: 10 days
isosceles trapezoid
-Opposite angles are congruent
-Consecutive angles are supplementary
-Opposite sides are congruent
-Diagonals bisect each other
-Diagonals of a rhombus are perpendicular and bisect each other
-Diagonals of a rhombus bisect the angles of the rhombus
-Diagonals of a rectangle are congruent and bisect each other
-Any properties true of a rhombus or a rectangle is true of a square
-Nonvertex angles of a kite are congruent
-Diagonals of a kite are perpendicular
-Diagonal between the vertex angles of a kite is the perpendicular
bisector of the other diagonal
-Vertex angles of a kite are bisected by the diagonal between them
-Consecutive angles between the bases of a trapezoid are
supplementary
-Base angles of an isosceles trapezoid are congruent
-Diagonals of an isosceles trapezoid are congruent
-Midsegment of a triangle is parallel to and half the length of the third
side
-The three midsegments of a triangle divide it into four congruent
triangles
properties are completed,
may need 1 additional day
of mixed quadrilaterals
Similar Figures: 13 days
-If two triangles are similar then the lengths of the corresponding
special segments are proportional to the lengths of the
corresponding sides
-Angle bisector divides the opposite side into two segments
whose lengths are in the same ratio as the sides of the angle
-A line parallel to a side of a triangle divides the other two sides
proportionally
-same with multiple lines
or flagpole using
mirrors and
shadows
any day after section 11.2,
depending on the weather
-In a right triangle, the altitude drawn from the right angle is the
geometric mean between the pieces of the hypotenuse
-In a right triangle with an altitude drawn from the right angle, a
leg is the geometric mean between the hypotenuse and the
portion of the hypotenuse adjacent to the let
Transformations: 13 days
translation, rotation, reflection, reflectional symmetry, rotational
symmetry, point symmetry
-The line of reflection is the perpendicular bisector of the
segment connecting the pre-image and image
-Reflections: orientation reversed, all measures preserved
-Translations: is the result of double reflection over parallel lines and
the magnitude is twice the distance between those lines; all
measures and orientation preserved
-Rotations: is the result of a double reflection over intersecting lines
and the magnitude is twice the angle formed by the lines; all
measures and orientation preserved
point after 7.1
-Rules for reflecting points and lines over the x-axis, y-axis, y=x,
and y=-x
-Discuss where the image would coincide with the pre-image
idea of equality - "point"
rule vs "equation" rule
-Define positive and negative degrees of rotation
-Rules for rotating 90, 180, and 270 degrees
-Composite of two rotations and magnitude, composite of two
translations and magnitude, composite of two reflections and
magnitue
-Using compositions to reflect over lines parallel to the x-axis, the
y-axis, y=x or y=-x
Right Triangles: 14 days
-Pythagorean Theorem
geometric mean
right using the Pythagorean Theorem
figures or prove conjectures
-Define: sine, cosine, and tangent
-Use sine, cosine, and tangent to find side lengths and angle
measures
total of 3 days split any
way
-Define: angle of elevation, angle of depression
Circles:13 days
tangency, concentric circles, arc, major and minor arcs, semicircle,
arc measure, central angle
-Measure of an arc is equal to the measure of its central angle
-Tangents from a common point are congruent
-Congruent chords form congruent central angles and intercepted
arcs
-The perpendicular from the center of a circle to a chord is the
bisector of the cord
-Congruent chords are equidistant from the center
-Perpendicular bisector of a chord passes through the center
-Inscribed angles that intercept the same or congruent arcs are
congruent
-Angles inscribed in a semicircle are right angles
-Opposite angles of a cyclic quadrilateral are supplementary
-Parallel lines intercept congruent arcs
of the measures of the intercepted arcs
-Measure of angle formed by two tangents, two secants, or a
secant and a tangent is half the difference of the measures of the
intercepted arcs
pg 333: 8
pg 339: 16,19
pg 343: 9
GSP pgs 355-
358
resources are investigations.
Any application of the
conjectures must be
supplemented
equals the product of the segments of the other
-When two secants intersect, the product of the outer secant
segment and the whole secant of one, is equal to the product of
the outer secant segment and the whole secant of the other
-When a secant and a tangent intersect, the product of the outer
secant segment and the whole secant is equal to the square of the
tangent
must be supplemented
One additional day should be
spent on combined practice
over the supplemented
material
Circumference and arc
length can be done with area
depending on when spring
break falls
Area:10 days
-Calculate areas of sector, segment, and annulus
circles, and right triangles
the problems where angles and
lengths of sides of right triangles
is necessary, or wait until after
8.2 and do all problems
-Define height/altitude of parallelogram (quadrilateral)
-Area of triangle using sine
-Area of regular polygons
length of the approximate length
of apothem. Must supplement
problems where exact length of
apothem is found/given.
Surface Area and Volume: 11 days
lateral faces, prism, pyramid, right, oblique, slant height, height
but no instruction necessary, maybe
assign after a test, or do together in
class
figures, as well as cylinders and cones